Thermodynamics: Calculating mass of air over a change in pressure/temperature

[MrNathan]

Homework Statement

A vessel of capacity 3 m3 contains air at a pressure of 1.5 bar and a
temperature of 25o C. Additional air is now pumped into the system until the
pressure rises to 30 bar and temperature rises to 60o C. The molar mass of air
is 28.968 g/mol.

Homework Equations

Calculate:
(i) The mass of air pumped into the system.

The Attempt at a Solution

I am not sure of the equation i should be using. I thought i should be using n=m/M but i do not know number of moles.

PS: This is my own revision and not homework. I have a University exam on monday and am struggling loads with thermodynamics. I feel I am missing a lot of the equations i should need, does anyone have a link to a list of them? The material my lecturers gave me is not very helpful.

Thanks
Any help appreciated

Nathan

 

[Andrew Mason]

Try PV = nRT

AM

 

[MrNathan]

what is n though? is this not a constant? i am not given it in the question

 

[MrNathan]

Oh i see, use pv = nRT to work out n.

ok, so from n = PV/RT, am i right in assuming the values of p, V and T are the differences?

n = pV/RT so n = (2850000 x 3)/(8.314 x 35)
n = 29382.45

m = nM so m = 851150.9

Im sure this is wrong as it seems too large.

 

[Andrew Mason]

Oh i see, use pv = nRT to work out n.

ok, so from n = PV/RT, am i right in assuming the values of p, V and T are the differences?

n = pV/RT so n = (2850000 x 3)/(8.314 x 35)
n = 29382.45

You have to be careful of the units. 1.5 bar is 150 kPa = 150000 N/m^2

Temperature has to be in Kelvin: 25 C = 298 K

So:

$$n = \frac{PV}{RT} = \frac{150000 \times 3}{8.314 \times 298} = 181.6 \text{moles}$$

which looks about right.

AM

 

[MrNathan]

ah ok. thanks for the help. like i said above, do you have a directory on this site, or know a link to one, of all the thermodynamics equations?